the lcm of two numbers is 60 and one of the numbers is 7 less than the other number, what are the numbers?
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the answer will have to be a number that can go into 60 so list the factors. 60:1,2,3,4,5,6,10,12,15,20,30,60.Then minus all the numbers by seven.whatever number has a sum that is divisible by 60 is your answer. I KNOW THIS IS LATE
the answer will have to be a number that can go into 60 so list the factors. 60:1,2,3,4,5,6,10,12,15,20,30,60.Then minus all the numbers by seven.whatever number has a sum that is divisible by 60 is your answer.
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To find the two numbers, we can use the fact that their least common multiple (LCM) is 60 and one of the numbers is 7 less than the other.
Let's assume the larger number is x and the smaller number is y.
Given that the LCM of x and y is 60, we know that the product of x and y divided by their greatest common divisor (GCD) results in 60. Mathematically, this can be represented as:
(x * y) / GCD(x, y) = 60
Now, since we also know that one number is 7 less than the other, we can express this as:
x = y + 7
Substituting this into the equation for the LCM, we get:
((y + 7) * y) / GCD(y + 7, y) = 60
Simplifying further, we can rewrite this as:
(y^2 + 7y) / GCD(y + 7, y) = 60
To determine the exact values of x and y, we would need to find the values of y that satisfy this equation. We can do this by trying different values of y and checking if the equation holds true.
Alternatively, we can use a computer program or an online LCM calculator to quickly identify the possible values of y. By plugging in these values into the equation x = y + 7, we can then find the corresponding values of x.